Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations

Matyas Barczy (1) , Mohamed Ben Alaya (2) , Ahmed Kebaier (3) , Gyula Pap (4)

1 Department of Applied Mathematics and Probability
2 LMRS - Laboratoire de Mathématiques Raphaël Salem
3 LAGA - Laboratoire Analyse, Géométrie et Applications
4 Eötvös Lorand University - Operations Research Department

We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable L\'evy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. In all cases we prove strong consistency of the MLE in question, in the subcritical case asymptotic normality, and in the supercritical case asymptotic mixed normality are shown as well. In the critical case the description of the asymptotic behavior of the MLE in question remains open.

Domains: Mathematics [math]; Statistics [math.ST]; Mathematics [math]; Probability [math.PR]

Matyas Barczy, Mohamed Ben Alaya, Ahmed Kebaier, Gyula Pap. Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations. Statistics, 2019, 53 (3), pp.533-568. ⟨10.1080/02331888.2019.1579216⟩. ⟨hal-02332449⟩